Mechanics 5 Edexcel Rotational stuff Watch

lordcrusade9
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A uniform square lamina of side 2l andmass m is rotating with angular speed w in a horizontal plane about a smooth fixed vertical axis through the centre of the lamina. A particle of mass 3m is held at a height l above the lamina. the particle is released and adheres to the lamina at a corner. Find the angular speed of the lamina.

Surely the particle add mass onto the lamina but its vertical velocity does not increase the angular speed of the lamina?
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steve10
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This question just seems to be about conservation of angular momentum.

I can't see any reason for giving the height (l) of the particle above the lamina. Its kinetic energy from falling is simply going to be absorbed by the lamina, but won't affect the rotational energy of it (the lamina).
What will affect the lamna will be the sudden addition of a mass at one of its corners. This is going to increase the inertia of the new lamina and hence reduce its angular velocity.
I would find the inertia of the lamina before and after the 3m mass attached itself and use conservation of angular momentum to work out the new angular velocity in terms of the old angular velocity.
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DFranklin
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Steve10: the particle has initial angular momentum too (relative to the axis of rotation).

Edit: no it doesn't, as pointed out below. I misunderstood the axis of rotation; it would help if I read the question properly. The line below is also wrong for the same reason.

(If you think about the case where the lamina isn't rotating, it's obvious that an off-centre impact is going to cause rotation).
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rnd
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(Original post by DFranklin)
If you think about the case where the lamina isn't rotating, it's obvious that an off-centre impact is going to cause rotation.
I don't get it. If the lamina is horizontal and not rotating why would dropping a particle on it cause rotation?
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DFranklin
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Ah flip - you're right; I assumed the rotation was in a vertical plane. Teach me to read the question properly...
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rnd
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(Original post by DFranklin)
Teach me to read the question properly...
Not reading the question is a sign of genius. or so I tell myself.
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steve10
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(Original post by rnd)
Not reading the question is a sign of genius. ...
Given that, there are times when I must be a multiple genius - a genii ??
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